$f(n) = n^{2}-6n-5+2(g(n))$ $g(n) = 5n+2$ $ g(f(-9)) = {?} $
Solution: First, let's solve for the value of the inner function, $f(-9)$ . Then we'll know what to plug into the outer function. $f(-9) = (-9)^{2}+(-6)(-9)-5+2(g(-9))$ To solve for the value of $f$ , we need to solve for the value of $g(-9)$ $g(-9) = (5)(-9)+2$ $g(-9) = -43$ That means $f(-9) = (-9)^{2}+(-6)(-9)-5+(2)(-43)$ $f(-9) = 44$ Now we know that $f(-9) = 44$ . Let's solve for $g(f(-9))$ , which is $g(44)$ $g(44) = (5)(44)+2$ $g(44) = 222$